I have two planes
$$2x+3-z=0$$
$$5y+xz=0$$
The intersection line of this planes can be found by solving the system above for $x$ and $y$, expressed by $z$(or $y$ and $z$ expressed by $x$). The result is
$$y=-\dfrac{1}{5}x(2x+3)$$
$$z= (2x+3)$$
Now each point of intersection line described by
$$(x,y,z)=(x,\space -\dfrac{1}{5}x(2x+3),\space (2x+3))$$
For example (0,0,3).
I wrote a javascript code using three.js to visualize that line.
function line(cena, x, y, z, xx, yy, zz, colorr) {
var geometryl=new THREE.Geometry();
geometryl.vertices.push(new THREE.Vector3( xx, yy, zz));
geometryl.vertices.push(new THREE.Vector3( x, y, z));
var materiall=new THREE.LineBasicMaterial( {
color: colorr
}
);
var line=new THREE.Line( geometryl, materiall);
cena.add( line);
return line;
}
var scene=new THREE.Scene();
var camera=new THREE.PerspectiveCamera( 45, window.innerWidth / window.innerHeight, 1, 10000);
var renderer=new THREE.WebGLRenderer();
renderer.setSize( window.innerWidth, window.innerHeight);
document.body.appendChild( renderer.domElement);
for(var i=-10;i<10;i++)
line(scene, i, (-1/5)*i*(2*i+3), 2*i+3, i+1, (-1/5)*(i+1)*(2*(i+1)+3), 2*(i+1)+3, 'white');
renderer.render( scene, camera);
What did I get:
Am I stupid, or two planes indeed can intersect the way I show?
English is not my native language, maybe I’m confused of a plane word? By plane I mean stuff that can be described by three dots, or two dots and vector. Plain is flat and straight. Or maybe we are talking about the same thing, but my math is bad and plane can be not “straight”? But seems this object better described by the word “surface”
Changed to
$$2x+3-z=0$$
$$5y+x+z=0$$
The intersection line of this planes
$$y=-\dfrac{3x}{5}-\dfrac{3}{5} $$
$$z= (2x+3)$$
The way it rocks: